Seattle has played six games this season and is still seeking its first victory.
Utah led for most of the night, but the game was close throughout the fourth quarter -- and it was tied, 101-101, going into the final minute, with Seattle having possession.
Seattle again turned the ball over, but Utah's Andrei Kirilenko lost it as well with six seconds to go.
That gave Durant, the second player taken in this year's draft, a chance to force overtime. Durant, however, missed a jumper.
Durant scored 20 points and Jeff Green had 19 for Seattle.
Boozer paced the Jazz with 27.